A note on downdating the Cholesky factorization

95. A. W. Bojanczyk, R. P. Brent, P. Van Dooren and F. R. de Hoog, A note on downdating the Cholesky factorization, SIAM J. Scientific and Statistical Computing 8 (1987), 210-221. MR 88d:65049.

A modified version appeared in Algorithms and Applications on Vector and Parallel Computers, Elsevier, Amsterdam, 1987, 307-323. MR 89i:65042, 89f:65002.

Abstract: dvi (3K), pdf (81K), ps (28K).

Paper: pdf (815K).


We analyse and compare three algorithms for "downdating" the Cholesky factorization of a positive definite matrix. Although the algorithms are closely related, their numerical properties differ. Two algorithms are stable in a certain "mixed" sense while the other is unstable. In addition to comparing the numerical properties of the algorithms, we compare their computational complexity and their suitability for implementation on parallel or vector computers.


For an application of downdating to the QR factorization of Toeplitz matrices, see [92].

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